A bandpass enclosure is more efficent in sub bass than a ported bass reflex enclosure.
It's common to find bandpass sub bass enclosures used for car entertainment music and video/dvds to give the low end rumble for movies,and low end thump for music.
And that driver being in a bandpass is twice as efficent as being in a ported bass reflex cabinet [of the same size' dimensions'].

P.S. A more efficent design is one which is more louder in the sub bass than other.Think of it like a light bulb [how much goes into light and how much is wasted as heat].Eg,thats why energy saver bulbs generate little heat and more light,that term is considered efficency.

Hope the bandpass subwoofer project works out ok with your main speakers[intergrates well]. Good Luck m8